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PROBLEM # 1.6 The current that flows past a point in space is t < 0...
(1 point) Consider the following initial value problem: y" + 36y= 0 <t< 5 t> 5 y(0) = 4, y'(0) = 0 Using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s) =
5. (20 pts). Solve the following initial-value problem: Ut + 2uuz - 0<x<, 0 <t<oo 0 1 <1 > 1 u(t,0) = Then draw the solution for different values of time.
(1 point) Compute the Laplace transform of fl) = 7, 10Sz<11 6t, if 11 Sz< 0 L{S}() =
1. Solve the initial-boundary value problem one = 4 for () <<3, t> 0, u(0,t) = u(3, 1) = 0 for t> 0, u(x,0) = 3x – 2” for 0 < x < 3. (30 pts.)
1. Discrete Fourier Analysis. Given the following periodic function: 50. 0<t<2s a) Find discrete time rot and amplitude y(rSi) values for y(t). Find time values t1, t2, ..tN with ot-0.2 s over the interval -2.0 to 1.8 s, amplitudes yl, y2, y3,.. .,yN. and N.
9. Solve the wave problem: 0 < x < T, t> 0; Utt: t2 0; u(T, t) = 0, u(0, t) = 0, 0 SST. u(x,0) = sin(10r), u(x, 0) = sin(4æ) + 2 sin(6x), Answer: sin(10r) sin(10t). 10 sin(4r) cos(4t) + 2 sin(6x) cos(6t) + u(x, t) =
(a) Let x(t) = 1 when 0 <t<1 and 0 for all other real t. Find and graph the following: (i) r(t -3). [5] (ii) c(t/2). (5] (iii) <((t-3)/2). [5] (iv) (t/2) – 3). [5]
= 0 over the domains 0<x<1 and t>0, where x is space and t is time at ax ди (1,1) = 0 ax Dirichlet and Neumann BCs are u(0, t)=80; Find the solution of the PDE that satisfies the given IC and BCs a. IC: u(x,0) 25sin (nx)
I need help with these Laplace problems:)
(1 point) Find the Laplace transform of <9 f(t) = { 0, " I(t - 9)?, 129 F(s) = (1 point) Find the inverse Laplace transform of e-75 F(s) = 52 – 2s – 15 f(t) = . (Use step(t-c) for uc(t).) (1 point) Find the Laplace transform of 0. f(t) t<5 112 – 10t + 30, 125 F(s) =
(1 point) Find the length of the curver r(t) = i +3t'j + tºk, 0<t</96 L